scholarly journals SWASHES: a compilation of shallow water analytic solutions for hydraulic and environmental studies

2012 ◽  
Vol 72 (3) ◽  
pp. 269-300 ◽  
Author(s):  
Olivier Delestre ◽  
Carine Lucas ◽  
Pierre-Antoine Ksinant ◽  
Frédéric Darboux ◽  
Christian Laguerre ◽  
...  
2013 ◽  
Vol 74 (3) ◽  
pp. 229-230 ◽  
Author(s):  
Olivier Delestre ◽  
Carine Lucas ◽  
Pierre-Antoine Ksinant ◽  
Frédéric Darboux ◽  
Christian Laguerre ◽  
...  

Water ◽  
2021 ◽  
Vol 13 (22) ◽  
pp. 3195
Author(s):  
Nan-Jing Wu ◽  
Yin-Ming Su ◽  
Shih-Chun Hsiao ◽  
Shin-Jye Liang ◽  
Tai-Wen Hsu

In this paper, an explicit time marching procedure for solving the non-hydrostatic shallow water equation (SWE) problems is developed. The procedure includes a process of prediction and several iterations of correction. In these processes, it is essential to accurately calculate the spatial derives of the physical quantities such as the temporal water depth, the average velocities in the horizontal and vertical directions, and the dynamic pressure at the bottom. The weighted-least-squares (WLS) meshless method is employed to calculate these spatial derivatives. Though the non-hydrostatic shallow water equations are two dimensional, on the focus of presenting this new time marching approach, we just use one dimensional benchmark problems to validate and demonstrate the stability and accuracy of the present model. Good agreements are found in the comparing the present numerical results with analytic solutions, experiment data, or other numerical results.


2011 ◽  
Vol 675 ◽  
pp. 1-26 ◽  
Author(s):  
R. ROTUNNO ◽  
J. B. KLEMP ◽  
G. H. BRYAN ◽  
D. J. MURAKI

Nearly all analytical models of lock-exchange flow are based on the shallow-water approximation. Since the latter approximation fails at the leading edges of the mutually intruding fluids of lock-exchange flow, solutions to the shallow-water equations can be obtained only through the specification of front conditions. In the present paper, analytic solutions to the shallow-water equations for non-Boussinesq lock-exchange flow are given for front conditions deriving from free-boundary arguments. Analytic solutions are also derived for other proposed front conditions – conditions which appear to the shallow-water system as forced boundary conditions. Both solutions to the shallow-water equations are compared with the numerical solutions of the Navier–Stokes equations and a mixture of successes and failures is recorded. The apparent success of some aspects of the forced solutions of the shallow-water equations, together with the fact that in a real fluid the density interface is a free boundary, shows the need for an improved theory of lock-exchange flow taking into account non-hydrostatic effects for density interfaces intersecting rigid boundaries.


Author(s):  
Yurii I. Shokin ◽  
Alexander D. Rychkov ◽  
Gayaz S. Khakimzyanov ◽  
Leonid B. Chubarov

AbstractIn the present paper we study features and abilities of the combined TVD+SPH method relative to problems of numerical simulation of long waves runup on a shore within the shallow water theory. The results obtained by this method are compared to analytic solutions and to the data of laboratory experiments. Examples of successful application of the TVD+SPH method are presented for the case of study of runup processes for weakly nonlinear and strongly nonlinear waves, and also for


2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Il Won Seo ◽  
Young Do Kim ◽  
Chang Geun Song

In this study, a shallow water flow code was developed and tested against four benchmark problems of practical relevance. The results demonstrated that as the eddy viscosity increased, the velocity slope along the spanwise direction decreased, and the larger roughness coefficient induced a higher flow depth over the channel width. The mass conservation rate was determined to be 99.2%. This value was measured by the variation of the total volume of the fluid after a cylinder break. As the Re increased to 10,000 in the internal recirculating flow problem, the intensity of the primary vortex had a clear trend toward the theoretically infinite Re value of −1.886. The computed values of the supercritical flow evolved by the oblique hydraulic jump agreed well with the analytic solutions within an error bound of 0.2%. The present model adopts the nonconservative form of shallow water equations. These equations are weighted by the SU/PG scheme and integrated by a fully implicit method, which can reproduce physical problems with various properties. The model provides excellent results under various flow conditions, and the solutions of benchmark tests can present criteria for the evaluation of various algorithmic approaches.


2020 ◽  
Author(s):  
Javier Gonzalez ◽  
Teresa Medialdea ◽  
Henrik Schiellerup ◽  
Irene Zananiri ◽  
Pedro Ferreira ◽  
...  

<p>The oceans and seas cover more than 70% of the planet, representing a promising new frontier for mineral resources exploration, and an enormous challenge for science and technology. Communities are demanding actions to address global climate change, and the necessary high- and green-technologies required for a transition from a carbon-based to green-energy-based world. The global ocean is at the core of these issues. The seabed mineral resources host the largest reserves on Earth for some critical metals like cobalt, tellurium, manganese, and the rare earth elements, critical for Industry. But seabed geology and ecosystems are widely unexplored, and new geological and environmental studies are required to address the impacts of potential mining activities. In addition, a regulatory framework for minerals extraction and marine spatial planning are necessary for seabed mining sector development.</p><p>The pan-European seas cover about 15 millions square kilometres in the Arctic and Atlantic oceans and the Mediterranean, Baltic, and Black seas, from shallow waters up to 6000 m water depth. Spanning a large diversity of environments and resource settings, including high and low temperature hydrothermal deposits, phosphorites, cobalt-rich ferromanganese crusts, and manganese nodules, deep-sea deposits are particularly attractive for their polymetallic nature with high contents of rare and critical metals. Moreover, shallow-water resources, like marine placer deposits, represent another source for many critical metals and gems. The GeoERA-MINDeSEA[1]  project is compiling data and genetic models for all these deposit types based on extensive studies, carried out previously, which include geophysical surveys, dredging stations, underwater photography and ROV surveys, and mineralogical, geochemical, and isotopic studies.</p><p>The preliminary MINDeSEA results show the potential of the pan-European seas for critical metals, and the enormous gaps of information covering vast marine sectors. More than 600 mineral occurrences are reported in the MINDeSEA database. Seamounts and banks in the Macaronesia sector (Portugal and Spain) and the Arctic ridges (Norway, Denmark, Iceland) show a high potential for Fe-Mn crusts, rich in energy-critical elements like Co but also Te, REEs, and Mn. Fe-Mn crusts are accompanied by phosphorites on the seafloor of continental shelves and slopes along the western continental margins. Seafloor polymetallic sulphides and metalliferous sediments precipitating from hot hydrothermal solutions and plumes are forming today in the Azores Islands (Portugal), the Arctic (Norway, Denmark) and, the Mediterranean volcanic arcs (Italy and Greece). They are among the most important marine resources for Cu, Zn, Ag, and Au. In addition, hydrothermal deposits may contain economic grades of Co, Sn, Ba, In, Bi, Te, Ga, and Ge. Placer deposits of chemically resistant and durable minerals have been discovered on shallow-water settings (<50 m water depth on estuaries, deltas, beaches) linked to the weathering of onshore rocks and ore deposits from the Variscan Belt (UK, France, Portugal, Spain). Finally, shallow-water concretions and nodules from the Arctic, Baltic, and Black Sea represent potential targets for metals exploration and environmental studies.</p><div><br><div> <p>[1] This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 731166</p> <p> </p> </div> </div>


2018 ◽  
Author(s):  
Ofer Shamir ◽  
Itamar Yacoby ◽  
Nathan Paldor

Abstract. The analytic wave-solutions obtained by Matsuno (1966) in his seminal work on equatorial waves provide a simple and informative way of assessing atmospheric and oceanic models by measuring the accuracy with which they simulate these waves. These solutions approximate the solutions of the shallow water equations on the sphere for small speeds of gravity waves such as those of the baroclinic modes in the atmosphere and ocean. This is in contrast to the solutions of the non-divergent barotropic vorticity equation, used in the Rossby-Haurwitz test case, which are only accurate for large speeds of gravity waves such as those of the barotropic mode. The proposed test case assigns specific values to the wave-parameters (gravity wave speed, zonal wave-number, meridional wave-mode and amplitude) for both planetary and inertia gravity waves, and confirms the accuracy of the simulation by employing Hovmöller diagrams and temporal and spatial spectra. The proposed test case is successfully applied to a standard finite-difference, equatorial, non-linear, shallow water model in spherical coordinates, which demonstrates that Matsuno’s wave-solutions can be accurately simulated for at least 10 wave-periods, which for oceanic planetary waves is nearly 1300 days. In order to facilitate the use of the proposed test case, we provide Matlab, Python and Fortran codes for computing the analytic solutions at any time on arbitrary latitude-longitude grids.


2003 ◽  
Vol 24 (9) ◽  
pp. 1081-1088 ◽  
Author(s):  
Huai Wen-xin ◽  
Y. Peter Sheng ◽  
T. Komatsu

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